In this paper, a nonlinear mathematical model has been constructed by deriving the equations of motion of a Rail Vehicle Bogie using Newton's law. The nonlinear formula is used to evaluate the wheel rail contact forces. The nonlinear profile of wheel and rail are taken into account. Also the lateral stiffness of the track is taken into consideration. The equations of motion are derived for (a) Bogie with conventional wheelset (b) Bogie with unconventional wheelset (independently rotating wheels). For lateral vibration, 7 degrees of freedom are considered. The degrees of freedom represent lateral and yaw movements of both the wheelsets and lateral, yaw and roll movements of the bogie. These equations of motion are transformed into a form suitable for numerical integration by Adam's method [9]. In the interest of computing economy, certain approximations have been introduced for calculating the creep forces. Sample results are given for a model of a typical railway vehicle used by the Indian Railways. The lateral dynamic response of the railway vehicle for both conventional and unconventional wheelset has been analyzed.